Calculus 1 (AP, Honors, Academic) Summer Assignment 2018

Transcription

1 Calculus (AP, Honors, Academic) Summer Assignment 08 The summer assignments for Calculus will reinforce some necessary Algebra and Precalculus skills. In order to be successful in Calculus, you must have certain prerequisite skills mastered. The Unit Circle for special angles must be memorized. You will be tested on the topics listed below. You will not be permitted to use a calculator during the test. Complete this practice over the summer. I recommend doing four problems each day. There are 9 problems. Show your work on looseleaf and graph paper. The packet will be collected on the first day of school. Be sure that your work is neat, well-organized and complete. You are encouraged to use any and all resource materials available to you such as your notebooks from previous math courses, math tetbooks found in the public and college libraries, and the Internet. As you complete the review eercises, you are preparing for the first test of the first quarter. Calculus (,, ) Summer assignment

2 Calculus (AP, Honors, Academic) Summer Assignment 0 Part Simplify. ( + + )( + ) + ( + + )( + ). ( )() (+5)() ( ) Rewrite in factored form. ( )( + ) ( + ). 8 ( 5) + ( 5) ( ) 5. ( + ) + ( + ) Solve for z in terms of and y. (z + y) + yz = 0 7. z + y + yz + y = y z = 8z z + y + yz + 7z = 0 Calculus (,, ) Summer assignment

3 Calculus (AP, Honors & Academic) Summer Assignment Part Solve the following. Epress answers as integers, simplified fractions, or simplified radicals. If no answer eists, eplain why in sentence form. Find the vertical asymptote of each function. A vertical asymptote of a rational function occurs at a domain value (-value) where the denominator is zero and the numerator is not zero f ( ) 9 f ) 9 ( f ( ) f ( ) f ( ) f ( ) f ( ) f ( ) sin f ( ) sin 0. f ( ) tan (Remember the Quotient Property of trig functions) Calculus (,, ) Summer assignment

4 Calculus (AP, Honors & Academic) Summer Assignment Part Solve the following. Epress answers as integers, simplified fractions, or simplified radicals. If no answer eists, eplain why in sentence form. Find the values of that make the functions equal zero.. f ( ). f ( ). f ( ). f ( ) cos for 0 5. f ( ) sin for 0. f ( ) sin for 0 7. f ( ) sec for 0 8. f ( ) sec sec tan for 0 Calculus (,, ) Summer assignment

5 Calculus (AP, Honors & Academic) Summer Assignment Part Solve the following. Epress answers as integers, simplified fractions, or simplified radicals. If no answer eists, eplain why in sentence form. Find the values of where (a) the function equals zero and (b) the function is undefined.. f ( ). f ( ) sin cos sin for 0. f ( ). f ( ) cos sin for 0 5. f ( ) Calculus (,, ) Summer assignment

6 Calculus (AP, Honors, Academic) Part 5 NO CALCULATOR: () Simplify, if possible: (a) 8 (b) (c) 8 () Solve for : (a) 7( ) (b) 0 0 (c) (e) ln 5 (f) log ( ) (g) e 0 (h) 5 (i) e 50 (j) 7 (k) 0.5( ) 0 (l) e e 0 (m) 5 9 (n) 7 (o) (p) (q) 0 Calculus (,, ) Summer assignment

7 () Using your knowledge of the unit circle, evaluate: (a) sin (b) sin 0 (c) (f) cos 0 (k) tan 0 (p) csc 0 (v) (g) (l) (q) sin cos (h) cos (i) tan (m) tan csc (r) sec 0 (n) (s) sin cos tan sec sin (w) cos 0 () sec 5 (e) sin 5 (j) cos 5 (o) tan (t) cot (u) 7 cot () Simplify the following trig epressions: (a) sin cot (b) tan csc cos (c) sec sin cos sin csc (5) Simplify without any negative eponents in the final answer: (a) 7 (b) (c) y 5 y 0 (g) 5 (h) (j) 0 y 7 (k) (e) 7 y 5 sin 7 0 (f) 8 (i) 9 y y () Rewrite in eponential form: (a) (b) 5 (7) Rewrite in radical form: (a) (b) (8) Simplify: (a) y 0 (b) 00 Calculus (,, ) Summer assignment

8 (9) Sketch the following equations as accurately as you can. Use your knowledge of the transformation rules. (a) y (b) y 7 (c) (f) (h) y (e) y y ( ) y ln (i) y ln y (g) (j) y sin (k) y sin (l) y e (m) y e (n) y e (o) y cos (p) y cos (q) y cos (r) y (s) y (t) y (u), 0 y (v), 0, y 5,, (0) Rewrite in eponential form: (a) log 9 (b) log () Rewrite in logarithmic form: (a) 5 0 (b) 8 () Evaluate: (a) log (b) log 5 (c) ln e (e) ln (f) log 0 ln (g) e ln e () Simplify, if possible: (a) ln 8 ln 5 (b) ln 0 ln (c) ln ln ln 500 ln 0 Calculus (,, ) Summer assignment

9 (e) (i) ln 5 ln e ln (f) (ln )(ln ) (g) ln( ) e (h) ln e sin () Rewrite without an eponent: ln (5) Rewrite using an eponent: ln () If you could use a calculator, how would you evaluate the following problems? (a) log 7 0 (b) log (7) Are the following epressions defined? Indicate yes or no. (a) (b) + when = 0 (c) 5 when = 5 0 when = (e) 8 when = 8 (f) when = 0 (g) ln (h) ln 0 (i) ln( ) (8) Indicate if the following statements are true or false. (a) The graph of y is equivalent to the graph of y. (b) The solutions for are the same as those for. (c) The graph of y is equivalent to the graph of y. (9) Given that f ( ) and g( ) sin, determine: (a) f (7) (b) g ( ) (c) f g f ( g( )) (e) g ( f ( )) (f) f ( f ( )) (g) f ( c) (h) h () where h( ) f ( ) (i) j( ) where j( ) f ( g( ) ) Calculus (,, ) Summer assignment